10 papers
Sparsity-Cone SDP Relaxations and Applications to Variable Fixing for Sparse Quadratic Programs
Di Hou, Thai P. D. Nguyen, Kim-Chuan Toh +1
Quadratic programs (QPs) with sparsity constraint are generally NP-hard, and their efficient global solution depends crucially on tractable tight convex relaxations. In this paper,…
A preconditioned augmented Lagrangian method for solving semidefinite programming problems
Tianyun Tang, Kim-Chuan Toh
In this work, we propose a preconditioned augmented Lagrangian method (ALM) for solving semidefinite programming (SDP) problems. The preconditioner is implemented via a weighted pe…
Gradient flow for finding E-optimal designs
Jieling Shi, Kim-Chuan Toh, Xin T. Tong +1
The -optimality criterion for a regression model maximizes the smallest eigenvalue of the information matrix and becomes non-differentiable when this eigenvalue has multiplicity…
Time-integrated Optimal Transport: A Robust Minimax Framework
Thai P. D. Nguyen, Hong T. M. Chu, Kim-Chuan Toh
Comparing time series in a principled manner requires capturing both temporal alignment and distributional similarity of features. Optimal transport (OT) has recently emerged as a…
A Low-rank Augmented Lagrangian Method for Polyhedral-SDP and Moment-SOS Relaxations of Polynomial Optimization
Di Hou, Tianyun Tang, Kim-Chuan Toh
Polynomial optimization problems (POPs) can be reformulated as geometric convex conic programs, as shown by Kim, Kojima, and Toh (SIOPT 30:1251-1273, 2020), though such formulation…
A Quadratically Convergent Alternating Projection Method for Nonconvex Sets
Nachuan Xiao, Shiwei Wang, Tianyun Tang +1
In this paper, we consider the feasibility problem, which aims to find a feasible point for the constraint set over a possibly non-regular subset…